Smeed and beyond
Predicting road death


Based on international road deaths figures gathered in the 1930s, Professor R J Smeed derived a formula for predicting road deaths. We examine the Smeed predictions and propose a more comprehensive and up-to-date formula.

Note that 2003 data is shown in several places on this page. 2003 data has not yet been published and the figures used are extrapolated from data from 16 counties as published in the press and on web sites. All other data is derived from official sources.

The Smeed formula
D = 300 (np2)1/3
D = annual road deaths
n = number of registered vehicles
p = population
The Smeed formula implies that road safety efforts are a waste of time because road deaths can simply be predicted from population figures. Fortunately for us, we have moved a long way from the Smeed predictions.
Here are the Smeed predictions:

As you can see in figure 1 above, the Smeed prediction was moving correctly and had approximately the right magnitude until about 1966. Since 1966 the Smeed prediction continues to rise, while the real road deaths have fallen quite reliably. By 2000, the Smeed prediction was about 4 times too high.

Figure 2 shows the relationship between the Smeed prediction and the actual number of road deaths. Between 1966 and about 1993 the real trend diverged steadily from the Smeed predicted trend. Since 1993 the divergence has been less marked.

Figure 3 again shows the Smeed trend diverging from the real trend. This time we have introduced the total vehicle mileage and calculated "rate" figures. "Rate" figures are based on events per billion vehicle km. This graph show the fatality rate - i.e. the number of road deaths per billion vehicle km. In 2,000 the Smeed derived rate would have been 29.5, while the true rate was 7.3.

Getting the hump

In the real world fatalities changed direction in the late 1960s. Smeed didn't predict this change, and there's a very simple and straightforward reason for the reversal. Allow us to explain...

We have had very regular growth in vehicle traffic since the earliest records. The pattern of growth approximates to a fixed increase in traffic every year. The value of the fixed increase is about 8.75 billion vehicle km per annum. The green trace in figure 4 above show this exact trend compared with real data (red trace). The slow-down in 1973 was the oil crisis. You can also clearly see the late 1980s economic boom and the early 1990s economic "bust". Nevertheless, the average rate of growth is remarkable constant.

This sort of pattern of growth shows on a conventional graph as a straight line. Such patterns may properly be described as "linear". The formula for the green line is:

TM = 38 + (year-1950) * 8.75
TM = total vehicle mileage in billion vehicle kilometres
year = present year

In order to derive the late 1960's fatality hump, "something" has to "swamp" the effect of the rise in traffic. Fortunately there's a very obvious mechanism that had exactly this effect. Engineering safety on the roads, and especially vehicle safety, have given us a regular fixed annual percentage improvement, worth about 5.7% per annum. This sort of growth is correctly termed "exponential".

In the mid to late 1960s the size of the percentage improvement in engineering safety became greater than the annual percentage increase in total mileage. This is why there's a hump - "pre-hump" the growth in annual mileage was dominant - "post-hump" the growth in engineering safety was dominant.

It is very much to be expected than an exponential trend will swamp a linear trend at some particular point.

You may notice that our calculated hump (green trend line) comes slightly earlier than the real data hump (red trend line). The main reason for this is that vehicle safety improvements have been accelerating. We relate this to greater annual spend by motor manufacturers on vehicle safety features. A more sophisticated model could easily take this further trend into account, but it certainly isn't necessary to include these subtle additional factors to understand the main relationships.

Fatality Rate

The two trends mentioned above (engineering safety improvements and traffic growth) are the main factors that combine to create our overall roads safety as indicated the the "fatality rate". In figure 6 we see the way the actual fatality rate has changed together with an idealised approximation based on the trends above.

We are extremely concerned about the recent divergence of the fatality rate from the former trend in recent years. In Figure 6 you can see the red data line diverging from the green "idealised" data line since 1993. Although it only looks like a small divergence, we believe that it is an extremely significant and important change, worth something like 6,000 lives lost to date.

Figure 7 plots exactly the same data as Figure 6, but this time the Y axis (vertical) scale is a log scale. The log scale has the advantage of showing exponential trends as a straight line. It is very plain to see that the red data line diverges from the green prediction line post 1993.

Figure 8 again show the same trend as figures 6 and 7, but this time we have "zoomed in" to the post 1993 period. The red data line is remarkably smooth which strongly indicates that the diverging trend is a real change rather than random fluctuation. We are especially concerned to note that for almost every year since 1993 the red data line has been turning further and further from the previous trend.

Safe Speed now firmly believes that the unexpected behaviour of the fatality and fatality rate trends are due to a dangerous and misguided road safety policy. See

and the latest general spreadsheet: 5500.xls

With unexplained road deaths running at some 1,200 per annum - one third of the total - we now feel fully justified in the claim: one third of roads fatalities are due to speed cameras (and the policies that support them).

Road Safety

We found it illuminating to calculate a road safety "input factor" for both the idealised model and also for the actual data. The results are shown in figure 9 above. These curves are calculated as follows:

Road Safety =  TM * 100 / D
D = Annual road deaths
TM = total annual mileage in bvkm
(In other words, this value is 100 times the reciprocal of the fatality rate: (100 / fatality rate))

It makes an interesting graph, and shows very clearly the worrying divergence from trend in recent years.

The Future

In Figure 10 we have extrapolated the long term trends to the year 2050. At Safe Speed we believe that such long term performance can and should be achieved. All we have to do is ensure that our policies and our culture are as good as they were from 1950 until 1993. By 2050 we would have reduced annual road deaths to 357 or so.

We believe that there are two main ways in which we should expect to be able to exceed these projections:

  • Increased spend on vehicle safety year on year.
  • Better "human" road safety policy based on a "health and safety" style approach to building the safety culture.
However present policy is doing terrible damage and has already put us a decade behind. If we want to see these improvements we must get back on track absolutely as soon as possible.
Update on Smeed

Safe Speed suggests the following approximate formula should be useful in predicting both road deaths and the rate of change of road death for any country. It can also be used to derive a "Road Safety Culture Factor" (CF) for any country.

               TM  * CF
D =  -----------------------
         1.057 (year - 1950)

                        D * 1.057 (year - 1950)
         CF =  ------------------------------------


D = annual road deaths
TM = Total vehicle mileage in bvkm
CF = Culture Factor
year = test year

The Culture Factor is set up so that a value of 100 represents good road safety performance. Less than 100 is better, and improving the CF to 50 would represent a halving of the road death toll. A larger CF indicates poorer performance.  

The GB Culture Factor stayed within about 20% of 100 from 1950 until 1993 and has been increasing since then. All other countries have a higher culture factor (as far as we know).

Data and references

This page has two directly related downloadable Excel 97 spreadsheets with full reference to data sources:

Smeed (figures 1, 2 and 3)

beyond (figures 4 to 10)


Smeed was wrong because he simply didn't allow for the massive advances in vehicle safety. (And why should he? The opportunities for improvement were unknown in those days.) 

Modern "speed kills" road safety policy is wrong because it does not allow for the negative side effects on the important aspects of the safety culture. We find this utterly shameful.

Overall road safety is clearly dominated by three main influences:

  • Engineering safety - and in turn engineering safety is dominated by vehicle safety
  • Opportunity for error - mainly dominated by total annual mileage
  • Average driver quality - mainly a result of national road safety culture
Of the three, only average driver quality is amenable to improvement by policy. Vehicle safety improvements will continue at a substantial pace driven by market forces.

Safe Speed calls for a "culture feeding" strategy based on reducing driver error. Such things have been achieved in vehicle fleets, in Police driver training and in industry.

What are we waiting for?


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Copyright © SafeSpeed 2004
Created 29/03/2004. Last update 30/03/2004